The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
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The standard deviation in a standard normal distribution is 1.
The standard deviation in a standard normal distribution is 1.
The standard normal distribution is a special case normal distribution, which has a mean of zero and a standard deviation of one.
Yes, the normal distribution, standard or not is always continuous.
The mean of a standard normal distribution is 0.